Lesson 5 HW, Statement Negation Drills

[FrannieVargas]

I'm currently working through chapter 5 HW and came across the Statement Negation Drill (pg 5-14) While I am doing well on this exercise and am best friends with the Opposition Construct, I'm having a difficult time understanding how to negate conditional statements. Helps please.

Loyally,
Frannie Vargas '12

[Dave Killoran]

Hi Frannie,

Thanks for the message. A conditional statement is negated by stating that the necessary condition is not necessary. Let's look at an example to see how it works.

Consider the following statement:

To get to the top of the building, you must take the stairs.

In this sentence, the author is claiming that for someone to get to the top of the building, it is necessary that they take the stairs. The diagram would be:

Top of the building --> stairs

To negate this statement, we would need to show that that the necessary condition (take the stairs) doesn't have to happen. That negation would appear as follows:

To get to the top of the building, you do not necessarily have to take the stairs.

Using your friend the Opposition Construct, you can see that the "must" in the first sentence turned into "not necessarily" when the statement was negated.

Here's another example:

Terence won't go skiing unless Mia goes skiing.

Diagram: Terence skiing --> Mia skiing

Negation: Terence can go skiing even if Mia does not go skiing.

Note that there are numerous ways to word that negation, so that example is just one phrasing. But, the key is to show that Terence can go without Mia having to go.

Please let me know if that helps. Thanks!

[AspenHerman]

Hi! I'm going to ressurct this question.

This one specifically revolves around number 4 (page 5-14)
Happiness is impossible unless we profess a commitment to freedom.
Using the unless equation...
Happiness commitment to freedom
Translated to plain english: If happiness is possible, then we profess a commitment to freedom.

I would expect the answer to be: If happiness is possible, then we do not necessarily profess a commitment to freedom.

However, the key says:
Even if we do not profess a commitment to freedom, happiness may still be possible.
(slash) commitment to freedom happiness may be possible

Is this another way to do it? Mistaken reversal, with an opposite (now) sufficient condition? Did I read/interpet something wrong?

Curious minds are wondering...

Aspen

[Rachael Wilkenfeld]

Hi Aspen,

I think you diagrammed the answer choice given incorrectly. Remember that the necessary condition can appear before the sufficient in a statement. Even if we do not express a commitment to freedom, happiness is possible would be

Happiness possible not nec. commitment to freedom

Hope that helps!

[AspenHerman]

Hi Aspen,

I think you diagrammed the answer choice given incorrectly. Remember that the necessary condition can appear before the sufficient in a statement. Even if we do not express a commitment to freedom, happiness is possible would be

Happiness possible not nec. commitment to freedom

Hope that helps!

Thank you for answering~

I was going off the "if". Now, I understand that "if" doesn't necessarily always have to signify a sufficient statement... so I guess that's where I went wrong, by trying to translate the answer from the key.
I guess I still have the concept down, and it's just differently stated in the key?

[Ryan Twomey]

Hey Aspen,

Yes. So the only way to negate a conditional statement in an assumption question answer choice is to say that the necessary condition isn't actually necessary.

Dave's two examples above provide a brilliant and simple description for how to negate conditional statements in assumption questions.

But first, I would recommend making sure you are perfect at mapping out conditional statements before worrying about how to negate them. Mapping out conditional statements should be memorized like the back of your hand. Then when you negate them you just say that the necessary condition could happen or could not happen even with the sufficient condition present.

I'll provide one example to add to Dave's. If my answer choice says:

Clouds------>Rain

Negating that answer choice would mean: it could be cloudy and then we have no idea if it rains or not.

I hope this makes sense, and I wish you all of the luck in your studies.

Best,
Ryan

[AspenHerman]

Hey Aspen,

Yes. So the only way to negate a conditional statement in an assumption question answer choice is to say that the necessary condition isn't actually necessary.

Dave's two examples above provide a brilliant and simple description for how to negate conditional statements in assumption questions.

But first, I would recommend making sure you are perfect at mapping out conditional statements before worrying about how to negate them. Mapping out conditional statements should be memorized like the back of your hand. Then when you negate them you just say that the necessary condition could happen or could not happen even with the sufficient condition present.

I'll provide one example to add to Dave's. If my answer choice says:

Clouds------>Rain

Negating that answer choice would mean: it could be cloudy and then we have no idea if it rains or not.

I hope this makes sense, and I wish you all of the luck in your studies.

Best,
Ryan

Thanks for responding. So, your response got me thinking... would "even if" be an indicator for the necessary condition? I'm noticing, amongst several examples, that an unless statement is negated to an "even if" statement.

Thanks!
Aspen

[Robert Carroll]

Aspen,

"Even if" is not a conditional indicator. In fact, it's the opposite - "even if" indicates there is no conditional relationship between two things. That's why every negation of an "unless" statement involved "even if" in your experience. Remember, as the Unless Equation teaches us, that "unless" indicates a conditional. If I say "I won't go to Scrooge's funeral unless lunch is provided", we diagram as:

go to funeral lunch provided

But take the statement "If I am to go to Scrooge's funeral, lunch must be provided". Diagram:

go to funeral lunch provided

So the two statements are identical. "Unless" is not the only way to express exactly the same conditional.

So if "even if" appears in the negation of an "unless" conditional, it will appear in the negation of any conditional at all. That's why you're seeing it every time, and why you can always express the negation of a conditional with an "even if" phrasing.

Robert Carroll

[AspenHerman]

Aspen,

"Even if" is not a conditional indicator. In fact, it's the opposite - "even if" indicates there is no conditional relationship between two things. That's why every negation of an "unless" statement involved "even if" in your experience. Remember, as the Unless Equation teaches us, that "unless" indicates a conditional. If I say "I won't go to Scrooge's funeral unless lunch is provided", we diagram as:

go to funeral lunch provided

But take the statement "If I am to go to Scrooge's funeral, lunch must be provided". Diagram:

go to funeral lunch provided

So the two statements are identical. "Unless" is not the only way to express exactly the same conditional.

So if "even if" appears in the negation of an "unless" conditional, it will appear in the negation of any conditional at all. That's why you're seeing it every time, and why you can always express the negation of a conditional with an "even if" phrasing.

Robert Carroll

Alright, thank you! I think I got it now.